I am not sure if I can explain the question correctly because I don't know the name of this mechanism in English.

This is my explanation attempt: In a house, a tube is expelling the air from the inside to the outside, and a tube is aspiring the air from the outside to the inside. The 2 tubes are interlaced in order to transmit the heat between their contents. The goal is to have a good thermal isolation between inside the house and outside:

When the house is more hot than the outside, the outgoing air is warming the incoming air.

When the house is more cold than the outside, the outgoing air is cooling the incoming air.

Question: In theory, what is the maximum efficiency of such thermal exchange? Could it be possible to reach something close to 1 or the upper bound of the efficiency is well under?

4 Answers
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The theoretical efficiency of these can reach 1, though note that for heat exchangers efficiency doesn't mean the same as for heat engines i.e. heat converted to work. For heat exchangers an efficiency of 1 just means the incoming air is heated to the same temperature as the air in the house and likewise for the outgoing air.

It's called either MVHR (Mechanical Ventilation with Heat Recovery) or HRV (Heat-recovery ventilation), depending on where you are in the world.

It possible to get a heat-exchange efficiency of between 90% and 100%, and there are several units on the market that achieve this.

It is possible to combine this with an air-source heat pump to get a nominal efficiency that exceeds 100%: in this case, the theoretical upper limit on the Coefficient of Performance (the version of efficiency we use for heat pumps) is given by Carnot's law.

According to my understanding of Physics and the laws of thermodynamics a heat exchanger efficiency of 100% (1) (where the incoming air temperature is raised to the same temperature as the outgoing air) is physically impossible as energy transfer can only occur where a temperature difference exists ! So, plainly, any such claim by heat exchanger manufacturers has got to be, to put it mildly, economical with the truth and must be taken with a very large pinch of Salt !!!!!

My 35 years as a Building Services Engineer and Consultant did not equip me to overule the laws of Physics and that will continue to make me very sceptical about plainly fanciful claims by equipment manufacturers.

Common sense must always be applied by competent system designers and that will always rely on adequate doses of scepticism.